By Snir Gazit
This paintings addresses dynamical facets of quantum criticality in area dimensions. It probes power scales: the amplitude (Higgs) mode, which describes fluctuations of the order parameter amplitude within the damaged symmetry part and the twin vortex superfluid stiffness. the implications show that the amplitude mode should be probed arbitrarily on the subject of criticality within the common line form of the scalar susceptibility and the optical conductivity. The hallmark of quantum criticality is the emergence of softening power scales close to the part transition. additionally, the writer employs the charge-vortex duality to teach that the capacitance of the Mott insulator close to the superfluid to insulator section transition serves as a explore for the twin vortex superfluid stiffness. The numerical equipment hired are defined intimately, specifically a trojan horse set of rules for O(N) relativistic types and techniques for numerical analytic continuation of quantum Monte Carlo info. The predictions got are quite appropriate to fresh experiments in chilly atomic structures and disordered superconductors.
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The capacitance measures the dielectric response of the insulator. Its divergence reflects the large particle-hole fluctuations near the transition. In the vortex description the insulator is a bose condensate of vortices, with a low frequency vortex conductivity σ˜ v (ωm ) = ρv /( 2 ωm ). As a consequence, ρv can be defined in terms of the capacitance by applying Eq. 1), ρv ≡ σq . 8) We shall use this important relation to test for CVD in the 2+1 dimensional O(2) field theory. 4 Methods A large scale QMC simulation of Eq.